Question

Rain is falling vertically with a speed of $4m/s$. After sometime, wind starts blowing with a speed of $3m/s$ in the north to south direction, in order to protect himself from a rain a man standing on the ground should hold his umbrella at an angle $\theta$ given by

Answer 1

Velocity of wind will be added to velocity of rain

Velocity of rain $\overrightarrow{V_r}=4(-\hat{j})m/s$

Velocity of wind $\overrightarrow{V_w}=3\left(\hat{i}\right)m/s$

Net velocity $\overrightarrow{V}=\overrightarrow{V_r}+\overrightarrow{V_w}$

$=3\hat{i}+(-4\hat{j})$

angle from vertical will be $\theta ={\tan }^{-1}\frac{3}{|-4|}={37}^o$.

${37}^o$ from vertical towards south